Understanding Exponentiation and Algebraic Identities

The video tutorial explains how to solve the expression 2^18 - 1 by breaking it down into simpler parts. It begins by splitting the exponent using the rule of exponents, then applies an algebraic identity to simplify the expression further. The tutorial continues with substituting known values and performing calculations to arrive at the final result. The process is explained step-by-step, ensuring clarity and understanding of each mathematical operation involved.

What is the first step in solving 2 to the power of 18 minus 1?

• Multiply 2 by 18

• Subtract 1 from the base

• Split the exponent into smaller parts

• Add 1 to the exponent

Which algebraic identity is used to simplify the expression?

• a^2 + b^2 = (a + b)(a - b)

• a^2 + b^2 = (a - b)(a + b)

• a^2 - b^2 = (a - b)(a + b)

• a^2 - b^2 = (a + b)(a - b)

What is the value of 2 to the power of 9?

• 1024

• 128

• 512

• 256

What is the purpose of using the identity a^2 - b^2 = (a + b)(a - b)?

• To increase the exponent

• To simplify the expression

• To change the base

• To add the terms

After substituting 2 to the power of 9, what are the two expressions formed?

• 514 and 512

• 512 and 510

• 513 and 511

• 515 and 513

What method is used to multiply the expressions 500 + 13 and 500 + 11?

• Direct Multiplication

• Cross Multiplication

• FOIL Method

• Distributive Method

What is the result of 500 times 500?

• 250,000,000

• 25,000

• 2,500,000

• 250,000

What is the sum of 500 times 24?

• 1,200,000

• 12,000

• 1,200

• 120,000

What is the final result of 2 to the power of 18 minus 1?

• 262,144

• 262,143

• 341,262

• 341,263

Which of the following is not a step in solving the expression?

• Adding the base

• Substituting values

• Using the FOIL method

• Splitting the exponent